Subspaces--Linear Algebra

I am trying to work on these proofs and I am having a hard time with this one.

Let V be a vector space and S={v1, v2, v3,…vk} be a set of vectors in V. Prove that span S is a subspace of V.

I am not really sure where to even start. I know what span and I know that in order to prove something is a subspace of something else you must show u+v is an element of W and c•u is an element of W. I just don't know what to do for this one.

I am trying to work on these proofs and I am having a hard time with this one.

Let V be a vector space and S={v1, v2, v3,…vk} be a set of vectors in V. Prove that span S is a subspace of V.

I am not really sure where to even start. I know what span and I know that in order to prove something is a subspace of something else you must show u+v is an element of W and c•u is an element of W. I just don't know what to do for this one.